Milnor invariants and edge-homotopy classification of clover links

We define Milnor numbers for clover links and show that for a clover link, if Milnor numbers of length ≤k   vanish, then Milnor numbers of length ≤2k+1≤2k+1 are well-defined. Moreover we prove that two clover links whose Milnor numbers of length ≤k   vanish are equivalent up to edge-homotopy and C2k+1C2k+1-equivalence if and only if those Milnor numbers of length ≤2k+1≤2k+1 are equal. In particular, we give an edge-homotopy classification of 3-clover links by their Milnor numbers of length ≤3.